簡易檢索 / 詳目顯示
| 研究生： |
劉彥迪 Yan-Di Liu |
|---|---|
| 論文名稱： |
用來解一個系統的等式與不等式的新平滑函數 New smoothing functions for solving a system of equalities and inequalities |
| 指導教授： |
陳界山
Chen, Jein-Shan |
| 學位類別： |
碩士 Master |
| 系所名稱： |
數學系 Department of Mathematics |
| 論文出版年： | 2014 |
| 畢業學年度： | 102 |
| 語文別： | 中文 |
| 論文頁數： | 18 |
| 中文關鍵詞： | 平滑函數 、系統的等式與不等式 、收斂 |
| 英文關鍵詞： | Smoothing function, system of equations and inequalities, convergence |
| 論文種類： | 學術論文 |
| 相關次數： | 點閱：187 下載：24 |
| 分享至: |
| 查詢本校圖書館目錄 查詢臺灣博碩士論文知識加值系統 勘誤回報 |
In this paper, we propose a family of new smoothing functions for solving a system of equalities and inequalities. We also investigate a monotone algorithm and show that it is globally and locally superlinearly convergent under suitable assumptions
[1] R. bhatia, Matrix Analysis, Springer-Verlag, New York, 1997
[2] J.W. Daniel, Newton’s method for nonlinear inequalities, Numerical Mathematics,vol. 21, pp. 381-387, 1973.
[3] R. A. Horn and C. R. Johnson, Matrix Analysis, Cambridge University Press,Cambridge, 1986.
[4] Z-H. Huang, Y. Zhang, and W. Wu, A smoothing-type algorithm for solving stsyem of inequalities, Journal of Computational and Applied Mathematics, vol. 220,pp. 355-363, 2008.
[5] D.Q. Mayne, E. Polak, and A.J. Heunis, Solving nonlinear inequalities in a finite number of iterations, Optimization Theory and Applications, vol. 33, pp. 207-221, 1981.
[6] M. Sahba, On the solution of nonlinear inequalities in a finite number of iterations,Numerical Mathematics, vol. 46, pp. 229-236, 1985.
[7] J.M. Schott, Matrix Analysis for Statistics, 2nd edition, John Wiley, New Jersey,2005.
[8] H-X. Ying, Z-H. Huang, and L. Qi, The convergence of a Levenberg-Marquard
method for the l2-norm solution of nonlinear inequalities, Numerical Functional Analysis and Optimization, vol. 29, pp. 687-716, 2008.
[9] Y. Zhang and Z-H. Huang, A nonmonotone smoothing-type algorithm for solving a system of equalities and inequalities, Journal of Computational and Applied
Mathematics, vol. 233, pp. 2312-2321, 2010.
[10] J. Zhu and B. Hao, A new non-interior continuation method for solving a system of equalities and inequalities, submitted manuscript, 2014.
[11] Robert G. Bartle, The Elements of Real Analysis, Second Edition
[12] S.L. HU , Z-H. Huang and P. Wang , A non-monotone smoothing Newton algorithm for solving nonlinear complementarity problems, Optimization Methods and
Software , vol. 24, pp. 447-460, 2009